Answer:
a. -0.92
b. 11% increase in demanded
Explanation:
Given p + 0.005x = 46, 0 ≤ p ≤ 46
Rewriting the demand equation by solving for x as follow:
0.005x = 46 - p
x = (46 - p) / 0.005
x = (46 / 0.005) - (1/0.005)p
x = 9,200 - 200p .................................................................... (1)
Differentiating equation (1) with respect to p, we have:
dx/dp = -200
We can now answer the two questions as follows:
a. Find the elasticity of demand when pequals$22.
To calculate elasticity of demand, the formula for calculating the elasticity of demand is used as follows:
E = Elasticity of demand = (p / x) * (dx / dp) ................... (2)
Since p = $22, we find x in equation (1) by substituting for p as follows:
x = 9,200 - 200 (22) = 4,800
Note that dx/dp = -200
Substituting the values into equation (2), we have:
E = (22 / 4,800) * (-200) = -0.92
Note: Since the absolute value of E i.e. |-0.92| is less than one, the demand is inelastic.
If the $22 price is decreased by 12%, what is the approximate percentage change in demand?
To do calculate this, we use the following formula for calculating the elasticity of demand:
E = % change in demand / % change in price ............. (3)
Since,
E = - 0.92
% change in price = -12%, or -0.12
Substituting the values into equation (3) and solve for % change in demand, we have:
-0.92 = % change in demand / -0.12
% change in demand = [-0.12] * [-0.92] = 0.11, or 11%
Therefore, the approximate percentage change in demand if the $22 price is decreased by 12% is 11% increase in demand.
